Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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PRIME BASES OF WEAKLY PRIME SUBMODULES AND THE WEAK RADICAL OF SUBMODULES

  • Received : 2012.03.27
  • Published : 2013.11.01
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Abstract

We will introduce and study the notion of prime bases for weakly prime submodules and utilize them to derive some formulas on the weak radical of submodules of a module. In particular, we will show that every one dimensional integral domain weakly satisfies the radical formula and state some necessary conditions on local integral domains which are semi-compatible or satisfy the radical formula and also on Noetherian rings which weakly satisfy the radical formula.

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References

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